In the special case when \(\theta = 1 / 2\)  and \(c = \sqrt{2 \mu }\) , the Uniform-LGI corresponds to the \(\mu \) -PL condition [1]}.
Here we give examples of functions satisfying the Uniform-LGI but not the PL condition: \(\mathcal {L} (w) = w^{2k}, k \in \mathbb {Z}^+\) . When \(k \ge 2\) , \(\mathcal {L} (w)\)  satisfies the Uniform-LGI on \(\mathbb {R}\)  with \(c = 2k\)  and \(\theta = 1 - 1 / 2k\) .
